\begin{align*} \gamma_0 & = E[X^3] - 3 \mu E[X^2] + 2 \mu^3\\ & = \int_a^b x^3 \frac{1}{b-a} dx - 3 \mu \frac{b^3-a^3}{3(b-a)} + 2 \left ( \frac{a+b}{2} \right )^3\\ & = \frac{x^4}{4(b-a)} right |_a^b - 3 \frac{a+b}{2} \cdot \frac{b^3-a^3}{3(b-a)} + 2 \frac{a^3 + 3a^2 b + 3a b^2 + b^3}{8} \\ & = \text{a miracle of algebra}\\ & = 0. \end{align*}